{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Hilbert 变换\n",
    "Hilbert 变换可用于形成解析信号。解析信号在通信领域中很有用，尤其是在带通信号处理中。scipy工具箱中的函数 hilbert 计算实数输入序列 x 的 Hilbert 变换，并返回相同长度的复数结果，即 y = hilbert(x)，其中 y 的实部是原始实数数据，虚部是实际 Hilbert 变换。在涉及到连续时间解析信号时，y 有时被称为解析信号。离散时间解析信号的关键属性是它的 Z 变换在单位圆的下半部分为 0。解析信号的许多应用都与此属性相关；例如，用解析信号避免带通采样操作的混叠效应。解析信号的幅值是原始信号的复包络。\n",
    "\n",
    "Hilbert 变换对实际数据作 90 度相移；正弦变为余弦，反之亦然。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1984fc1d960>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy.signal import hilbert\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "t = np.arange(0,1,1/1024)\n",
    "x = np.sin(2*np.pi*60*t)\n",
    "y = hilbert(x)\n",
    "\n",
    "plt.plot(t[1:50],y.real[1:50],label = 'Real Part')\n",
    "plt.plot(t[1:50],y.imag[1:50],label = 'Imaginary Part')\n",
    "plt.axis([0,0.05,-1.1,2])\n",
    "plt.legend(loc = 'upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "解析信号可用于计算时间序列的瞬时属性，即时间序列在任一时间点的属性。该过程要求信号是单分量的。"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
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